A right-angled triangle abc , formed from a metallic wire, travels at a uniform speed v in its plane. A uniform magnetic field B is present in the perpendicular direction. Determine the induced emf in the segment ab .

Step-by-step solution

The motional emf induced in a conductor is given by E = ( v B ) d l . The velocity of the loop is v = v i and the uniform magnetic field is B = B k (directed out of the plane). The magnetic force per unit charge is v B = (v i ) (B k ) = -vB j . This indicates that the induced electric field is directed downwards along the negative y-axis. For the segment ab , the effective length perpendicular to the velocity is its projection on the y-axis, which is the length bc . Thus, the magnitude of the induced emf in the seg